1. Field of the Invention
The present invention is related to the field of signal processing methods for oil well logging tools. More specifically, the present invention relates to signal processing methods for enhancing the resolution of nuclear magnetic resonance (NMR) measurements.
2. Background Art
Oil well logging tools include nuclear magnetic resonance (NMR) instruments. NMR instruments can be used to determine properties of earth formations, such as the fractional volume of pore space, the fractional volume of mobile fluid filling the pore space, and the porosity of earth formations. General background of NMR well logging is described in U.S. Pat. No. 6,140,817, assigned to the assignee hereof.
A typical NMR logging tool comprises a permanent magnet, which is used to align the nuclei of interest along its magnetic field, and an antenna, which is used to provide radio frequency (RF) pulses and to act as a receiver for the resulting resonance signals. The RF pulses transmitted through the antenna produce a magnetic field which realigns the nuclei in a different orientation. In a typical application, the RF pulse strength is controlled such that the nuclei are realigned onto a plane which is perpendicular to the direction of the magnetic field generated by the permanent magnet.
Such RF pulse is called a 90-degree pulse. Once in this perpendicular plane, the interactions between the static magnetic field and the nuclei cause these nuclei to precess around the static magnetic field axis with a characteristic frequency called Larmor frequency. The precessing of these nuclei produces signals that are detected by the antenna. In the absence of further perturbation, these nuclei will gradually return to their steady state, in which their spins are aligned with the static field generated by the permanent magnet. The process of this return to the steady state is referred to as the spin-lattice relaxation and is defined by a life time called T1. If the nuclei are kept in the perpendicular plane (e.g., by using a series of pulses as in CPMG sequence or a spin-lock sequence), the signals generated by these nuclei will decay exponentially by another mechanism, the spin-spin relaxation, which is defined by a different life time, T2. The T1 and T2 values reflect the chemical and physical properties of the observed nuclei. Therefore, they can provide information as to the properties and the environment of the nuclei.
The signals measured by nuclear magnetic resonance (NMR) logging tools typically arise from the selected nuclei present in the probed volume. Because hydrogen nuclei are the most abundant and easily detectable, most NMR logging tools are tuned to detect hydrogen resonance signals (form either water or hydrocarbons). These hydrogen nuclei have different dynamic properties (e.g., diffusion rate and rotation rate) that are dependent on their environments. The different dynamic properties of these nuclei manifest themselves in different nuclear spin relaxation times (i.e., spin-lattice relaxation time (T1) and spinxe2x80x94spin relaxation time (T2)). For example, Hydrogen nuclei in viscous oils have relatively short relaxation times whereas hydrogen nuclei in light oils possess relatively long relaxation times. Furthermore, the hydrogen nuclei in the free water typically have longer relaxation times than those in the bound water. Consequently, these differing NMR relaxation times can provide information on properties of the earth formations.
Most NMR logging tools measure the spin-spin relaxation times (T2) to derive the properties of the earth formations. The T2 relaxation is often measured from a train of spin-echoes that are generated with a series of pulses such as the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence or some variant of this. The CPMG pulse sequence is well known in the art. [See Meiboom, S., Gill, D., 1958, xe2x80x9cModified Spin Echo Method for Measuring Nuclear Relaxation Times,xe2x80x9d Review of Scientific Instruments, 29, 688-91]. FIG. 2 shows a CPMG sequence, which is typically composed of a 90-degree pulse followed by a series of 180-degree pulses with a fixed delay time between them. The initial 90-degree pulse aligns the nuclear spins in the plane perpendicular to the magnetic field generated by the permanent magnet. The successive 180-degree pulses keep these spins roughly in this plane for the duration of the measurement The proportion of nuclear spins in the transverse plane decays mainly via the spinxe2x80x94spin relaxation (T2) pathway. Thus, one can derive the T2 relaxation time by analyzing the exponential decay of the spin-echo magnitude.
The fast on-and-off pulses used in the CPMG sequence generate acoustic waves in the antenna by an effect known as the xe2x80x9cLorenz force.xe2x80x9d The antenna returns to its original shape in a series of damped mechanical oscillations in a process referred to as xe2x80x9cmagnetoacoustic ringing.xe2x80x9d Ringing can induce large voltages in the antenna which interfere with the measurement of the voltages induced by the nuclear spins. In addition, the RF pulses can also cause magnetostriction in the permanent magnet, which is a deformation of the magnet. In the process of returning to its original shape, the magnet generates a series of damped mechanical oscillations in a process known as xe2x80x9cmagnetostrictive ringing.xe2x80x9d In addition, the antenna/detectors often have inherent electronic offsets, which cause the baseline of the detected signals to deviate from the zero value. In order to cancel the electronic offsets and antenna ringing it is customary to combine two CPMG measurements of opposite phase. These pairwise-combined measurements (herein, measurements denote the detected signal amplitudes) are called phase-alternate-pair (PAP) echo trains and these constitute the datasets that are submitted to processing.
PAPs may be acquired successively or sequentially. In successive acquisition, each measurement consists of a complete PAP measurement, which includes two opposite-phased CPMG measurements, and each PAP measurement is independent of the preceding and the following PAP measurements. The sampling interval (with respect to wellbore length/depth) in successive acquisition is the distance traveled by the NMR logging tool during the acquisition of one complete PAP sequence. Thus, the axial resolution (herein, axial means along the axis of the wellbore) achievable by the successive acquisition method equals the antenna length plus the distance traveled by the NMR logging tool during the acquisition of one PAP sequence.
In contrast, with a sequential acquisition, every individual CPMG measurement contributes to two PAPs. In the first PAP a particular CPMG is combined with its preceding CPMG, which necessarily has opposite phase. In the second PAP it is combined with the following CPMG, which also has opposite phase. [Herein, measurements that are pairwise-combined from sequentially acquired data, like PAP, will be referred to as sequentially pairwise-combined measurements.] The sampling interval (with respect to the wellbore length/depth) in sequential acquisition is the distance traveled by the NMR logging tool during the acquisition of one CPMG sequence, rather than a PAP sequence (which contains two CPMG sequences). Thus, the sampling interval for a sequential acquisition is roughly half that of a successive acquisition. However, the axial resolution of a sequential PAP measurement is identical to that of a successive PAP because it takes two consecutive CPMG data sets to produce a PAP measurement in a sequential acquisition. Sequential PAP acquisition, as implemented on the CMR-PLUS NMR tool, is described in xe2x80x9cAn Improved NMR Tool Design for Faster Logging,xe2x80x9d Society of Professional Well Log Analysts (SPWLA) 40th Annual Logging Symposium, paper CC (1999).
Although PAP acquisition provides a convenient means for removing electronic offsets and ringing, it degrades the axial resolution of the NMR measurement. This loss of resolution is particularly acute for non-overlapping CPMG measurements, as in the above-described sequential and successive methods. Because it takes two CPMG measurements to produce a PAP measurement in the above-described methods, the axial resolution of a PAP measurement is approximately twice that of each individual CPMG measurement. In situations where thin bed identification and characterization are important, this loss of resolution limits data interpretation. The invention disclosed herein provides a method to recover the axial resolution of NMR data and processed logs from sequential PAP data so that an axial resolution of single CPMG measurements (i.e. one antenna length) is achieved.
A related method for deriving high-resolution permeability estimates from NMR log data is disclosed in U.S. patent application Ser. No. 09/397,581, filed on Sep. 16, 1999, and entitled xe2x80x9cEstimating Permeability.xe2x80x9d The technique involves summing all echoes generated in a CPMG train and applying an empirical calibration of this quantity to derive a permeability estimate. This method provides final logs with effective axial resolution equal to that of the original PAP data.
The methods of the present invention relate to methods for retrieving corrected individual measurement from sequentially pairwise-combined measurements. Such sequentially pairwise-combined measurements may include phase-alternated-pair (PAP) NMR measurements from well logging. One of the methods comprises providing an initial estimate for a first one of the corrected individual measurements, deriving temporary estimates for other ones of the corrected individual measurements by subtracting the initial estimate from the first sequentially pairwise-combined measurements to produce an estimate for a second one of the corrected individual measurements, and repeating the subtraction from each of the next sequentially pairwise-combined measurements until temporary estimates for each of the corrected individual measurements are obtained, and correcting errors in the temporary estimates to generate error-corrected estimates by filtering an alternating error component associated with the initial estimate.
Another method is for obtaining resolution-enhanced nuclear magnetic resonance well logging data. The method comprises acquiring individual measurements while moving the nuclear magnetic resonance well logging instrument along the wellbore, combining the individual measurements to form phase-alternated-pair measurements, and solving simultaneous equations to generate error-corrected estimates, wherein the simultaneous equations comprise equations describing the phase-alternated-pair measurements and an additional equation denoting a zero value of a dot product of a vector containing an alternating function and a vector containing the error-corrected estimates.
The methods may be applied to any sequentially pairwise-combined data such as PAP echo data from NMR well logging, or logs derived from these data, to generate a new data set or logs which correspond to single measurements such as the single depth level CPMG measurements from NMR logging, thereby enhancing the resolution of a measurement.